Find the greatest integer value of b for which the expression (9x^3+4x^2+11x+7)/(x^2+bx+68) has a domain of all real numbers.
The discriminant of x^2 + bx + 68 must be < 0
So
b^2 - 4(1) (68) < 0
b^2 - 272 < 0
b^2 < 272
This will be true when -sqrt (272) < x < sqrt (272)
Greatest integer value for b = floor[ sqrt (272) ] = 16
